GATE (TF) Textile 2022 Question Paper Solution | GATE/2022/TF/44

Question 44 (Textile Technology & Fibre Science)

The Gibb’s free energy equation for a system undergoing phase transition is given by ΔG = ΔH – TΔS, where ΔG is the change in Gibb’s free energy, ΔH is the change in enthalpy, ΔS is the change in entropy and T is the temperature in Kelvin. During melting transition, two systems A and B, show no difference in ΔH but B exhibits 10 % lower ΔS than A. The ratio of melting temperature of B to that of A (rounded off to 2 decimal places) is __.

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Given in the question-
ΔG = ΔH – TΔS

Given
ΔH_a=ΔH_b
and

ΔS_b=ΔS_a-10% \times ΔS_a

ΔS_b=ΔS_a-0.1 \times ΔS_a

ΔS_b=0.9 \times ΔS_a

Now,

ΔG_a=ΔG _b

ΔH_a-T_a\times ΔS_a=ΔH_b-T_b \times ΔS_b

here, ΔH_a=ΔH_b
So,

-T_a\times ΔS_a=-T_b \times ΔS_b

Here,
ΔS_b=0.9 \times ΔS_a

-T_a\times ΔS_a=-T_b \times 0.9 \times ΔS_a

-T_a=-T_b \times 0.9

\frac{T_b}{T_a}=\frac{1}{0.9}

\frac{T_b}{T_a}=1.11 (Ans)

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